相关论文: Mean-field and graph limits for collective dynamic…

In this paper we consider the modeling of opinion dynamics over time dependent large scale networks. A kinetic description of the agents' distribution over the evolving network is considered which combines an opinion update based on binary…

In this paper, we investigate the interaction of two populations with a large number of indistinguishable agents. The problem consists in two levels: the interaction between agents of a same population, and the interaction between the two…

We introduce a 2-state opinion dynamics model where agents evolve by majority rule. In each update, a group of agents is specified whose members then all adopt the local majority state. In the mean-field limit, where a group consists of…

We investigate a dynamical model of opinion formation in which an individual's opinion is influenced by interactions with a group of other agents. We introduce a bias towards one of the opinions in a manner not considered earlier to the…

We present an opinion dynamics model framework discarding two common assumptions in the literature: (a) that there is direct influence between beliefs of neighbouring agents, and (b) that agent belief is static in the absence of social…

We study discrete-time, finite-state mean-field games (MFGs) under model uncertainty, where agents face ambiguity about the state transition probabilities. Each agent maximizes its expected payoff against the worst-case transitions within…

Modelling efforts in opinion dynamics have to a large extent ignored that opinion exchange between individuals can also have an effect on how willing they are to express their opinion publicly. Here, we introduce a model of public opinion…

We study a time-delayed variant of the Hegselmann-Krause opinion formation model featuring a small group of leaders and a large group of non-leaders. In this model, leaders influence all agents but only interact among themselves. At the…

This paper focuses on the role of a government of a large population of interacting agents as a mean field optimal control problem derived from deterministic finite agent dynamics. The control problems are constrained by a PDE of…

We consider two-opinion voter models on dense dynamic random graphs. Our goal is to understand and describe the occurrence of consensus versus polarisation over long periods of time. The former means that all vertices have the same opinion,…

In this work, we systematically investigate mean field games and mean field type control problems with multiple populations using a coupled system of forward-backward stochastic differential equations of McKean-Vlasov type stemming from…

We investigate the effects of external and autonomous global interaction fields on an adaptive network of social agents with an opinion formation dynamics based on a simple imitation rule. We study the competition between global fields and…

The statement of the mean field approximation theorem in the mean field theory of Markov processes particularly targets the behaviour of population processes with an unbounded number of agents. However, in most real-world engineering…

The spread of an epidemic disease and the population's collective behavioural response are deeply intertwined, influencing each other's evolution. Such a co-evolution typically has been overlooked in mathematical models, limiting their…

A broad range of dynamical systems involve multi-body interactions, or group interactions, which may not be encoded in traditional graphical structures. In this work, we focus on a canonical example from opinion dynamics, the Majority Rule,…

We consider mean-field control problems in discrete time with discounted reward, infinite time horizon and compact state and action space. The existence of optimal policies is shown and the limiting mean-field problem is derived when the…

This paper is concerned with developing mean-field game models for the evolution of epidemics. Specifically, an agent's decision -- to be socially active in the midst of an epidemic -- is modeled as a mean-field game with health-related…

The mean-field limit in a weakly interacting stochastic many-particle system for multiple population species in the whole space is proved. The limiting system consists of cross-diffusion equations, modeling the segregation of populations.…

The formation of opinions in a large population is governed by endogenous (human interactions) and exogenous (media influence) factors. In the analysis of opinion evolution in a large population, decision making rules can be approximated…

Empirically derived continuum models of collective behavior among large populations of dynamic agents are a subject of intense study in several fields, including biology, engineering and finance. We formulate and study a mean-field game…